Adaptive optical systems in the form of adaptive mirrors for CO2 or Nd:YAG lasers are known, with which corrections to the focus position and beam diameter of a laser beam can be carried out in real time, in order, for example, to permit a controlled laser processing of workpieces. Adaptive mirrors can include a deformable mirrored plate that is rapidly and specifically deformed by a piezo actuator so that the focal length of the adaptive mirror can be continuously adjusted. The mirrored plates are available with a highly reflective coating for CO2 lasers (10.6 μm) or for Nd:YAG lasers (1.06 μm).